Answer:
a
The mass of blood is ![m= 5.7876kg](https://tex.z-dn.net/?f=m%3D%205.7876kg)
b
The number of blood cells is
Explanation:
From the question we are told that
The volume of blood is ![V_b = 5.46 \ L = \frac{5.46}{1000} = 0.00546m^3](https://tex.z-dn.net/?f=V_b%20%3D%205.46%20%5C%20L%20%3D%20%5Cfrac%7B5.46%7D%7B1000%7D%20%3D%200.00546m%5E3)
The density of the blood is ![\rho_b = 1060 kg/m^3](https://tex.z-dn.net/?f=%5Crho_b%20%3D%201060%20kg%2Fm%5E3)
% of blood that is cell is = 45.0%
% of the blood that is plasma is = 55.0%
density of blood cell is ![\rho_d = 1125kg/m^3](https://tex.z-dn.net/?f=%5Crho_d%20%3D%201125kg%2Fm%5E3)
% of cell that are white is = 1%
% of cell that is red is = 99%
The diameter of the red blood cell is = ![7.5 \mu m = 7.5*10^{-6}m](https://tex.z-dn.net/?f=7.5%20%5Cmu%20m%20%3D%207.5%2A10%5E%7B-6%7Dm)
The radius of the red blood cell is ![= \frac{7.5*10^{-6}}{2} = 3.75*10^{-6}m](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B7.5%2A10%5E%7B-6%7D%7D%7B2%7D%20%3D%203.75%2A10%5E%7B-6%7Dm)
Generally the mass is mathematically represented as
![m = \rho_b * V_b](https://tex.z-dn.net/?f=m%20%3D%20%5Crho_b%20%2A%20V_b)
Substituting value
![m = 1060 * 0.00546](https://tex.z-dn.net/?f=m%20%3D%201060%20%2A%200.00546)
![m= 5.7876kg](https://tex.z-dn.net/?f=m%3D%205.7876kg)
Mass of cell is
= 45% of m
= 0.45 * 5,7876
= 2.60442 kg
The volume of cells is
= ![\frac{m_c}{\rho_d}](https://tex.z-dn.net/?f=%5Cfrac%7Bm_c%7D%7B%5Crho_d%7D)
![= \frac{2.60442}{1125}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2.60442%7D%7B1125%7D)
![= 2.315 *10^{-3} m^3](https://tex.z-dn.net/?f=%3D%202.315%20%2A10%5E%7B-3%7D%20m%5E3)
The volume of white blood cell is
= 1% of volume of cells
![= \frac{1}{100} * 2.315*10^{-3}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B100%7D%20%2A%202.315%2A10%5E%7B-3%7D)
![= 2.315*10^{-5}m^3](https://tex.z-dn.net/?f=%3D%202.315%2A10%5E%7B-5%7Dm%5E3)
The volume of a single cell is ![V_s = 4 \pi r^3](https://tex.z-dn.net/?f=V_s%20%3D%204%20%5Cpi%20r%5E3)
![= 4*(3.142) * (3.75*10^{-6})^3](https://tex.z-dn.net/?f=%3D%204%2A%283.142%29%20%2A%20%283.75%2A10%5E%7B-6%7D%29%5E3)
![= 2.21*10^{-16}m^3](https://tex.z-dn.net/?f=%3D%202.21%2A10%5E%7B-16%7Dm%5E3)
The volume of red blood cells is ![V_r = V_c - V_w](https://tex.z-dn.net/?f=V_r%20%3D%20V_c%20-%20V_w)
![=2.315*10^{-3} - 2.315*10^{-5}](https://tex.z-dn.net/?f=%3D2.315%2A10%5E%7B-3%7D%20-%202.315%2A10%5E%7B-5%7D)
![= 2.29*10^{-3}m^3](https://tex.z-dn.net/?f=%3D%202.29%2A10%5E%7B-3%7Dm%5E3)
The number of red blood cell is ![= \frac{V_r}{V_s}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7BV_r%7D%7BV_s%7D)
![= \frac{2.29 *10^{-3}}{2.21*10^{-16}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2.29%20%2A10%5E%7B-3%7D%7D%7B2.21%2A10%5E%7B-16%7D%7D)
![= 1.037*10^{13}](https://tex.z-dn.net/?f=%3D%201.037%2A10%5E%7B13%7D)
The Number of white blood cell is ![=\frac{V_w}{V_s}](https://tex.z-dn.net/?f=%3D%5Cfrac%7BV_w%7D%7BV_s%7D)
![= \frac{2.315 * 10^{-5}}{2.21*10^{-16}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2.315%20%2A%2010%5E%7B-5%7D%7D%7B2.21%2A10%5E%7B-16%7D%7D)
![= 1.04*10^{11}](https://tex.z-dn.net/?f=%3D%201.04%2A10%5E%7B11%7D)
The total number of blood cells is ![N_t= 1.037*10^{13} + 1.04*10^{11}](https://tex.z-dn.net/?f=N_t%3D%201.037%2A10%5E%7B13%7D%20%2B%201.04%2A10%5E%7B11%7D)